The invention relates to a printing cylinder for a printing machine, or printing sleeve for forming a printing cylinder, which printing cylinder or printing sleeve comprises a plurality of cups for forming a supporting inner structure for the printing cylinder or printing sleeve, which plurality of cups comprises a central disc and a radially outer edge, with the radially outer edges of the plurality of cups together defining a substantially cylindrical surface. A printing cylinder or printing sleeve of this type is designed to be accommodated in a printing machine, such as an offset printing machine. The term printing cylinder is understood to refer inter alia to both a plate cylinder which carries the image to be printed, and to a cylinder which transfers ink from the plate cylinder to a web or substrate web, such as paper or film/foil material, via a so-called rubber blanket. A printing sleeve is a printing cylinder which comprises a cylindrical aperture which runs concentrically around the centre axis of the printing cylinder for accommodating a cylinder shaft. The printing sleeve may be fixedly connected to the respective cylinder shaft, or detachably connected to the cylinder shaft. In the latter case, the cylinder shaft is often fixedly connected to the printing machine and is also referred to as a mandrel.
EP-A2-0,127,953, at FIG. 11 thereof, shows a printing sleeve for a printing cylinder. The respective printing sleeve comprises a plurality of cups. Each of the cups has radial wall parts. On the outer edge of the radial wall part, there are first and second cylindrical wall parts. The second cylindrical wall parts are on an outer edge of the cups for forming a cylindrical outer surface of the printing cylinder. In this case, it should be noted that this is not the outermost surface of the printing cylinder, as there is still a rubber layer which runs around the outer surface of the common cups. The outer diameter of the first cylindrical wall parts is substantially equal to the inner diameter of the second cylindrical wall parts. As a result, the second cylindrical wall part of a first cup can be pushed over the first cylindrical wall part of a second cup in order to form a cup connection. This known printing sleeve has the drawback that it is difficult to produce.